$CATEGORY: Maths - TicTacLearn/4. Quadratic equations/4. Quadratic equations--Quadratic Equations

//Multiple Choice

The quadratic formula is used to find the roots of the equation\: {
~ \(ax+b\=0\)
= \(ax^2+bx+c\=0\)
~ \(ax^3+bx2+c\=0\)
~ \(ax^2+bx\=0\)
}

In the quadratic formula, the term inside the square root, \(b^2−4ac\) , is called\: {
~ Root
= Discriminant
~ Coefficient
~ Quadratic expression
}

If the discriminant \(b^2−4ac\)  is negative, then the quadratic equation has\: {
~ Two real and distinct roots
~ Two equal roots
= No real roots
~ Infinite solutions
}

If the quadratic equation \(2x^2−3x+1\=0\)  is solved using the quadratic formula, then the value of aaa is\: {
~ 1
= 2
~ -3
~ 0
}

If \(b^2−4ac\) , the roots of the quadratic equation are\: {
~ Real and distinct
= Real and equal
~ Complex
~ No roots
}

The roots of the quadratic equation \(x^2−4x+4\=0\)  using the quadratic formula are\: {
= 2, 2
~ -2, 2
~ 1, 4
~ No real roots
}

//True or False

The quadratic formula can be used to solve any quadratic equation. {T}

The quadratic formula is applicable only when the discriminant is positive. {F}

If \(b^2−4ac\=0\), the equation has two distinct real roots. {F}

The discriminant determines the nature of the roots of a quadratic equation. {T}

If \(b^2−4ac<0\) , the equation has no real solutions. {T}

The quadratic formula works only when a≠0. {T}

//Numericals



//Fill in the blanks

The quadratic formula is used to solve __________ equations. {
~ Linear
= Quadratic
~ Cubic
~ None of these)
}

The term \(b^2−4ac\) is called the __________ of the quadratic equation. {
~ Root
~ Coefficient
= Discriminant
~ None of these)
}

If \(b^2−4ac>0\) , then the quadratic equation has __________ roots. {
~ Two equal
= Two distinct real
~ No real
~ None of these)
}

If \(b^2−4ac\=0\) , then the roots of the quadratic equation are __________. {
~ Real and distinct
= Equal
~ No real
~ Imaginary)
}

If \(b^2−4ac<0\) , then the quadratic equation has __________ solutions. {
= No real
~ Two real and equal
~ Two real and distinct
~ None of these)
}

The roots of the equation \(x^2−6x+9\=0\),using the quadratic formula are __________. {
= 3, 3
~ -3, 3
~ 1, 6
~ No real roots
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=\(b^2−4ac\) -> Discriminant
=\(b^2−4ac\) \= 0 -> Two equal roots
=\(b^2−4ac\) > 0 -> Two distinct real roots
=\(b^2−4ac\) < 0 -> No real roots
}



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